To determine petroleum reserves, build geological models and develop optimal depletion plans, it is useful to know the distribution of sand and shale throughout the reservoir as well as the associated porosity of those rocks. Hydrocarbons (e.g., oil or gas) that are located in sand that is low porosity or poorly connected are much harder to drain than higher porosity, blocky sands. By sending acoustic waves through the subsurface and then recording the reflected waves that are returned, it is possible to obtain an image of the structure of the subsurface called the seismic reflectivity. As part of the data processing, the reflectivity profiles are often organized to form regularly spaced lines in two orthogonal directions that together comprise a 3-dimensional volume of the earth. A system of mathematical equations can be constructed that relate the amplitude of the seismic response to the intrinsic structure of the rocks that are reflecting the waves. Inversion methods can then be used to solve all of these equations simultaneously. (Inversion is any process whereby for a quantity y known to depend on one or more variables x, the values of x corresponding to measured values of y are inferred.) Current inversion methods obtain impedances or other attributes from seismic data, but none directly obtain porosity and shale volume (vshale) or clay content estimates. Shale or clay acts as a barrier to hydrocarbon flow, and their pore spaces are typically filled with water rather than hydrocarbons. Even when their pore spaces do contain hydrocarbons, it is very hard to extract such oil. What is not shale or clay in the siliciclastic depositional systems generally is sand. Thus, identifying the sands and the amount of connectivity between regions of sand is a major requirement for efficient reservoir production.
The amplitudes of reflected seismic waves that have traveled through the subsurface are related to changes in the elastic parameters (such as P and S impedances, P and S-wave velocities, and/or density) of the rocks between one layer and the next, as well as the angle of incidence with which the wave impinged on the boundary. Consequently, changes in amplitude as a function of receiver offset (AVO) can be used to infer information about these elastic properties. To take advantage of this phenomenon, subsets of seismic reflection data corresponding to particular offsets (or angles) or small groups of offsets (or angles) can be processed into what are called angle stacks. (“Offset” is the distance between a receiver and the seismic source.)
A commonly used method for determining vshale (i.e., clay content) and porosity from seismic reflection data (or attributes of the seismic data) is to invert angle stacks to obtain elastic properties (such as P and S impedances, P and S-wave velocities, and/or density) and then to look for relationships between those inverted parameters and the actual parameters of interest (i.e., lithologic parameters such as the porosity of the rock and whether it is a sand or a shale). This is a two-step process and has the disadvantage that the seismic reflectivity is related mathematically to elastic properties rather than the actual parameters of interest. Textbooks with the mathematical details of AVO include Aki and Richards, Quantitative Seismology, W. H. Freeman and Co, (1980) and Castagna and Backus, Offset-dependent reflectivity-theory and practice of AVO analysis, Society of Exploration Geophysicists (1993). Details of how to perform elastic inversion are contained in many papers, including D. Cooke and W. Schneider, “Generalized linear inversion of reflection seismic data”, Geophysics 48, 665-676, (1983); and J. Helgesen and M Landro, “Estimation of elastic parameters from AVO effects in the Tau-P Domain”, Geophysical Prospecting 41, 341-355, (1993); and J. Simmons and M. Backus, “Waveform-based AVO inversion and AVO prediction-error”, Geophysics 61, 1575-1588, (1996). Other publications describe methods of relating elastic parameters obtained in elastic inversion to the lithologic parameters of interest, for example, G. Lortzer and Berkhout, “An integrated approach to lithologic inversion-Part I: Theory”, Geophysics 57, 233-244 (1992). Some publications discuss both pieces together—elastic inversion followed by some sort of lithology inversion or transformation, for example, Pan, et al., “An integrated target-oriented prestack elastic waveform inversion”, Geophysics 59, 1392-1404 (1994); Martinez, et al., “Complex Reservoir Characterization by Multiparameter Constrained inversion”, Reservoir Geophysics, ed. By Sheriff, 224-234, (1992); J. Brac, et al., “Inversion with a priori information: an approach to integrated stratigraphic interpretation”, Reservoir Geophysics, ed. Sheriff, p 251-258, (1992); and M. Landro and A. Buland, “Target-oriented AVO inversion of data from Valhall and Hod fields,” The Leading Edge, 855-861 (1995). However, none of these papers proposes inverting the angle stacks of seismic reflection data directly for the compositional parameters of interest.
AVO techniques have also been the subject of a number of prior patents. U.S. Pat. No. 5,583,825 to Carrazone, et al. provides a number of literature references and discusses many of these prior patents. All of them involve predictions of the P-wave and S-wave reflectivities from full stack data rather than angle stacks. U.S. Pat. No. 6,665,615 to Van Riel et al. describe joint inversion of angle stacks to obtain elastic parameters (e.g., P-impedance, S-impedance, P-wave velocity, S-wave velocity, and density) with a method that requires simultaneously inverting multiple offsets from multiple trace locations in order to stabilize the result. In that same patent they also suggest the possibility of inverting compositional parameters (e.g., porosity and vshale) from seismic data using angle stacks, however, the inventors do not describe how such an inversion would be mathematically constructed and successfully accomplished.
Another class of methods for predicting clay content and porosity from seismic data uses pattern recognition, often implemented with neural networks, to relate changes in amplitude as a function of receiver offset with changes in lithology or porosity in the subsurface as described in, for example, Hampson, et al., “Use of multi-attribute transforms to predict log properties from seismic data”, Geophysics 66, 220-236 (2001). These methods use a training set to identify patterns between the well and the seismic data and then classify the remainder of the seismic data set according to the patterns observed in the training set. Consequently, the training set needs to contain a set of relationships that span the entire range of possible relationships that might be found in the reservoir (i.e., the training set requires examples from wells that have penetrated different sections of the reservoir in order to train the network competently). In regions of limited well control the relationships derived in this manner cannot be used with confidence. With sufficient well control, probabilistic neural networks can be very good interpolators (although generally terrible extrapolators). In regions of limited of well control, they are unreliable interpolators and worse extrapolators.
A method is needed for obtaining porosity and vshale estimates directly from inversion of seismic data. To reduce computational complexity, the method should be applicable to multiple offsets at a single trace location. Such a method would offer significant cost reduction over existing methods, and would provide more accurate lithology predictions which should reduce the number of dry holes drilled and improve well placement. The present invention satisfies this need.